Mathematics, 23.07.2019 07:00 JazzyJo2580
The vertices of a hyperbola are at (-5, -2) and (-5, 12) and the point (-5, 30) is one of its foci. what is the equation of its hyperbola
Answers: 1
![\bf \begin{cases} h=-5\\ k=5\\ a=7\\ c=25 \end{cases}\implies \cfrac{(y-5)^2}{7^2}-\cfrac{[x-(-5)]^2}{b}=1 \\\\\\ \cfrac{(y-5)^2}{7^2}-\cfrac{(x+5)^2}{b}=1\\\\ -------------------------------\\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b\implies \sqrt{25^2-7^2}=b \\\\\\ \sqrt{625-49}=b\implies \sqrt{576}=b\implies 24=b\\\\ -------------------------------\\\\ \cfrac{(y-5)^2}{7^2}-\cfrac{(x+5)^2}{24^2}=1\implies \cfrac{(y-5)^2}{49}-\cfrac{(x+5)^2}{576}=1](/tpl/images/0122/5244/ba80c.png)
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The vertices of a hyperbola are at (-5, -2) and (-5, 12) and the point (-5, 30) is one of its foci....
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